There is no place left for "old politics" in the trade unions, David Miliband has said, as he backed his brother's efforts to reform Labour's relationship with its biggest backers.

The former foreign secretary said Ed Miliband was doing the right thing as Labour leader by changing the way unions fund the party, as new allegations surfaced about Unite's tactics in the Scottish constituency of Falkirk.

Asked about the reforms, David Miliband told the BBC's Andrew Marr Show: "It's so big that Ed was right to say that he wants to reform the relationship with the unions. Because the truth is the leadership of the party has got to represent the whole country. Working people have an important stake, it's important to bring them in, but what you call 'old politics', rightly has no place, obviously."

Ed Miliband is facing fresh pressure to publish a report on Unite's actions during the process to select a Labour candidate in the Falkirk byelection. Labour commissioned an investigation into allegations of vote-rigging but concluded that there was no wrongdoing and cleared all Unite officials. Unite has repeatedly denied any wrongdoing.

However, the Sunday Times has obtained a Unite document designed to rebut allegations of vote-rigging, which suggests party investigators found "evidence that signatures were forged" and potential new members being allegedly coerced or "badgered" into signing direct debit bank forms for joining Labour.

On Sunday, Len McCLuskey, the general secretary of Unite, condemned the "disgraceful and despicable attacks on his union following publication of the allegations. He told the BBC's Sunday Politics that it had already been shown there was no case to answer.

"The truth of the matter is this is a track being laid by Tory central office," he said.

Speaking on the same programme, Chuka Umunna, the shadow business secretary, said police were now looking at fresh allegations about Falkirk and Labour would look at what to do after that.

However, he rejected calls for the report on Falkirk to be published, saying it was not right to ask people to give evidence to investigators in confidence and then reveal their disclosures.

A senior Labour source said no one should forget that Miliband was implementing "the biggest single reform in a generation" to the party's relationship with the unions.

Last week, the Labour leader was forced to condemn any "intimidatory tactics" used by unions in industrial disputes, after Unite members were accused of personally targeting Ineos bosses during the row over pay and conditions at Grangemouth.

Miliband said the same codes of behaviour were true for unions and employers, after the Daily Mail published allegations that family members of Ineos directors were intimidated by union tactics.

Unite has defended its right to use "leverage" tactics against companies, and McCluskey has dismissed any suggestion that some of his union's members were involved in bullying.

McCluskey said his union believed it was legitimate to confront "faceless directors … who destroy communities".

However, the incident has sparked a debate about the use of leverage tactics, which the union said involve asking "all interested parties to make moral and ethical decisions about their future relations with an employer who we believe is acting immorally".